Nuprl Lemma : compose-strict-inc
∀s,f:StrictInc. (s o f ∈ StrictInc)
Proof
Definitions occuring in Statement :
strict-inc: StrictInc,
compose: f o g,
all: ∀x:A. B[x],
member: t ∈ T
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
strict-inc: StrictInc,
uall: ∀[x:A]. B[x],
nat: ℕ,
so_lambda: λ2x.t[x],
subtype_rel: A ⊆r B,
uimplies: b supposing a,
le: A ≤ B,
and: P ∧ Q,
less_than': less_than'(a;b),
false: False,
not: ¬A,
implies: P ⇒ Q,
prop: ℙ,
so_apply: x[s],
compose: f o g,
int_seg: {i..j-},
lelt: i ≤ j < k,
guard: {T},
ge: i ≥ j ,
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
top: Top
Lemmas referenced :
lelt_wf,
int_formula_prop_wf,
int_formula_prop_not_lemma,
int_term_value_var_lemma,
int_term_value_constant_lemma,
int_formula_prop_le_lemma,
int_formula_prop_and_lemma,
intformnot_wf,
itermVar_wf,
itermConstant_wf,
intformle_wf,
intformand_wf,
satisfiable-full-omega-tt,
le_wf,
decidable__le,
nat_properties,
int_seg_properties,
strict-inc_wf,
false_wf,
int_seg_subtype_nat,
less_than_wf,
all_wf,
int_seg_wf,
nat_wf,
compose_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
sqequalHypSubstitution,
setElimination,
thin,
rename,
dependent_set_memberEquality,
lemma_by_obid,
isectElimination,
hypothesis,
hypothesisEquality,
natural_numberEquality,
sqequalRule,
lambdaEquality,
applyEquality,
independent_isectElimination,
independent_pairFormation,
because_Cache,
dependent_functionElimination,
productElimination,
unionElimination,
equalityTransitivity,
equalitySymmetry,
setEquality,
intEquality,
dependent_pairFormation,
int_eqEquality,
isect_memberEquality,
voidElimination,
voidEquality,
computeAll
Latex:
\mforall{}s,f:StrictInc. (s o f \mmember{} StrictInc)
Date html generated:
2016_05_14-PM-09_47_32
Last ObjectModification:
2016_01_15-PM-10_54_26
Theory : continuity
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