Nuprl Lemma : mFOL-rename_wf
∀[fmla:mFOL()]. ∀[old,new:ℤ]. (mFOL-rename(fmla;old;new) ∈ mFOL())
Proof
Definitions occuring in Statement :
mFOL-rename: mFOL-rename(fmla;old;new),
mFOL: mFOL(),
uall: ∀[x:A]. B[x],
member: t ∈ T,
int: ℤ
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
mFOL-rename: mFOL-rename(fmla;old;new),
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
so_lambda: so_lambda(x,y,z,w,v.t[x; y; z; w; v]),
so_apply: x[s1;s2;s3;s4;s5],
so_lambda: so_lambda(x,y,z,w.t[x; y; z; w]),
so_apply: x[s1;s2;s3;s4]
Lemmas referenced :
mFOL_ind_wf_simple,
mFOL_wf,
mFOatomic_wf,
map_wf,
ifthenelse_wf,
eq_int_wf,
list_wf,
mFOconnect_wf,
mFOquant_wf,
bool_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
hypothesisEquality,
lambdaEquality,
intEquality,
atomEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
because_Cache
Latex:
\mforall{}[fmla:mFOL()]. \mforall{}[old,new:\mBbbZ{}]. (mFOL-rename(fmla;old;new) \mmember{} mFOL())
Date html generated:
2016_05_15-PM-10_14_53
Last ObjectModification:
2015_12_27-PM-06_32_14
Theory : minimal-first-order-logic
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