Nuprl Lemma : FOL-subst_wf
∀[fmla:mFOL()]. ∀[nw,old:ℤ]. (fmla[nw/old] ∈ mFOL())
Proof
Definitions occuring in Statement :
FOL-subst: fmla[nw/old],
mFOL: mFOL(),
uall: ∀[x:A]. B[x],
member: t ∈ T,
int: ℤ
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
FOL-subst: fmla[nw/old],
all: ∀x:A. B[x],
subtype_rel: A ⊆r B,
and: P ∧ Q,
prop: ℙ,
uimplies: b supposing a,
squash: ↓T,
true: True
Lemmas referenced :
mFOL-rename_wf,
FOL-rename-bound-to-avoid_wf,
cons_wf,
nil_wf,
equal_wf,
list_wf,
mFOL-freevars_wf,
length_wf,
FOL-abstract_wf,
subtype_rel-equal,
AbstractFOFormula+_wf,
l_disjoint_wf,
mFOL-boundvars_wf,
mFOL_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
dependent_functionElimination,
hypothesisEquality,
intEquality,
because_Cache,
hypothesis,
applyEquality,
lambdaEquality,
setElimination,
rename,
setEquality,
productEquality,
instantiate,
cumulativity,
universeEquality,
applyLambdaEquality,
independent_isectElimination,
imageElimination,
equalitySymmetry,
natural_numberEquality,
imageMemberEquality,
baseClosed,
axiomEquality,
equalityTransitivity,
isect_memberEquality
Latex:
\mforall{}[fmla:mFOL()]. \mforall{}[nw,old:\mBbbZ{}]. (fmla[nw/old] \mmember{} mFOL())
Date html generated:
2018_05_21-PM-10_24_30
Last ObjectModification:
2017_07_26-PM-06_38_34
Theory : minimal-first-order-logic
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