Nuprl Lemma : type-incr-chain_wf
type-incr-chain{i:l}() ∈ 𝕌'
Proof
Definitions occuring in Statement :
type-incr-chain: type-incr-chain{i:l}(),
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
type-incr-chain: type-incr-chain{i:l}(),
member: t ∈ T,
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
so_lambda: λ2x.t[x],
nat: ℕ,
ge: i ≥ j ,
all: ∀x:A. B[x],
decidable: Dec(P),
or: P ∨ Q,
uimplies: b supposing a,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
implies: P ⇒ Q,
not: ¬A,
top: Top,
and: P ∧ Q,
prop: ℙ,
so_apply: x[s]
Lemmas referenced :
le_wf,
int_formula_prop_wf,
int_term_value_var_lemma,
int_term_value_add_lemma,
int_term_value_constant_lemma,
int_formula_prop_le_lemma,
int_formula_prop_not_lemma,
int_formula_prop_and_lemma,
itermVar_wf,
itermAdd_wf,
itermConstant_wf,
intformle_wf,
intformnot_wf,
intformand_wf,
satisfiable-full-omega-tt,
decidable__le,
nat_properties,
subtype_rel_wf,
all_wf,
nat_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
setEquality,
functionEquality,
cut,
lemma_by_obid,
hypothesis,
applyEquality,
thin,
lambdaEquality,
cumulativity,
hypothesisEquality,
universeEquality,
sqequalHypSubstitution,
isectElimination,
because_Cache,
dependent_set_memberEquality,
addEquality,
setElimination,
rename,
natural_numberEquality,
dependent_functionElimination,
unionElimination,
independent_isectElimination,
dependent_pairFormation,
int_eqEquality,
intEquality,
isect_memberEquality,
voidElimination,
voidEquality,
independent_pairFormation,
computeAll
Latex:
type-incr-chain\{i:l\}() \mmember{} \mBbbU{}'
Date html generated:
2016_05_15-PM-06_51_34
Last ObjectModification:
2016_01_16-AM-09_50_47
Theory : general
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