Nuprl Lemma : order-type-less-maximal
∀x:WFTRO{i:l}(). (x order-type-less() max-WO{i:l}())
Proof
Definitions occuring in Statement :
max-WO: max-WO{i:l}(),
WFTRO: WFTRO{i:l}(),
order-type-less: order-type-less(),
infix_ap: x f y,
all: ∀x:A. B[x]
Definitions unfolded in proof :
max-WO: max-WO{i:l}(),
all: ∀x:A. B[x],
member: t ∈ T,
WFTRO: WFTRO{i:l}(),
order-type-less: order-type-less(),
infix_ap: x f y,
spreadn: spread3,
WFO: WFO{i:l}(),
DCC: DCC(T;<),
not: ¬A,
implies: P ⇒ Q,
false: False,
prop: ℙ,
uall: ∀[x:A]. B[x],
so_lambda: λ2x.t[x],
nat: ℕ,
ge: i ≥ j ,
decidable: Dec(P),
or: P ∨ Q,
uimplies: b supposing a,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
top: Top,
and: P ∧ Q,
subtype_rel: A ⊆r B,
so_apply: x[s],
pi1: fst(t),
order-preserving: order-preserving(A;B;a1,a2.R1[a1; a2];b1,b2.R2[b1; b2];f),
cand: A c∧ B,
trans: Trans(T;x,y.E[x; y])
Lemmas referenced :
WFTRO_wf,
equal_wf,
nat_wf,
all_wf,
infix_ap_wf,
nat_properties,
decidable__le,
satisfiable-full-omega-tt,
intformand_wf,
intformnot_wf,
intformle_wf,
itermConstant_wf,
itermAdd_wf,
itermVar_wf,
int_formula_prop_and_lemma,
int_formula_prop_not_lemma,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
int_term_value_add_lemma,
int_term_value_var_lemma,
int_formula_prop_wf,
le_wf,
pi1_wf_top,
DCC_wf,
exists_wf,
set_wf,
subtype_rel_product,
top_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
introduction,
extract_by_obid,
hypothesis,
sqequalHypSubstitution,
productElimination,
thin,
sqequalRule,
dependent_functionElimination,
lambdaEquality,
because_Cache,
isectElimination,
equalityTransitivity,
equalitySymmetry,
hypothesisEquality,
independent_functionElimination,
voidElimination,
instantiate,
cumulativity,
universeEquality,
functionExtensionality,
applyEquality,
dependent_set_memberEquality,
addEquality,
setElimination,
rename,
natural_numberEquality,
unionElimination,
independent_isectElimination,
dependent_pairFormation,
int_eqEquality,
intEquality,
isect_memberEquality,
voidEquality,
independent_pairFormation,
computeAll,
productEquality,
independent_pairEquality,
functionEquality,
dependent_pairEquality,
setEquality,
addLevel,
hyp_replacement,
levelHypothesis
Latex:
\mforall{}x:WFTRO\{i:l\}(). (x order-type-less() max-WO\{i:l\}())
Date html generated:
2018_05_21-PM-07_15_03
Last ObjectModification:
2017_07_26-PM-05_03_46
Theory : general
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