Nuprl Lemma : consistent-model-fun_wf
∀[Gamma:mFOL() List]. ∀[x:ℕ]. ∀[L:(ℕ × ℕ) List]. (consistent-model-fun(Gamma;x;L) ∈ ℙ)
Proof
Definitions occuring in Statement :
consistent-model-fun: consistent-model-fun(Gamma;x;L),
mFOL: mFOL(),
list: T List,
nat: ℕ,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
product: x:A × B[x]
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
consistent-model-fun: consistent-model-fun(Gamma;x;L),
let: let,
prop: ℙ,
and: P ∧ Q,
nat: ℕ,
int_seg: {i..j-},
lelt: i ≤ j < k,
le: A ≤ B,
uimplies: b supposing a,
so_lambda: λ2x.t[x],
all: ∀x:A. B[x],
so_apply: x[s],
or: P ∨ Q
Lemmas referenced :
less_than_wf,
length_wf,
mFOL_wf,
or_wf,
assert_wf,
mFOquant?_wf,
context-lookup_wf,
lelt_wf,
equal-wf-T-base,
bool_wf,
mFOquant-isall_wf,
l_all_wf2,
nat_wf,
l_member_wf,
equal_wf,
FOL-subst_wf,
mFOquant-body_wf,
mFOquant-var_wf,
mFOconnect?_wf,
not_wf,
mFOconnect-knd_wf,
mFOconnect-left_wf,
mFOconnect-right_wf,
list_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
productEquality,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
setElimination,
rename,
because_Cache,
hypothesis,
hypothesisEquality,
dependent_set_memberEquality,
independent_pairFormation,
productElimination,
independent_isectElimination,
baseClosed,
lambdaEquality,
lambdaFormation,
independent_pairEquality,
setEquality,
atomEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality
Latex:
\mforall{}[Gamma:mFOL() List]. \mforall{}[x:\mBbbN{}]. \mforall{}[L:(\mBbbN{} \mtimes{} \mBbbN{}) List]. (consistent-model-fun(Gamma;x;L) \mmember{} \mBbbP{})
Date html generated:
2018_05_21-PM-10_41_20
Last ObjectModification:
2017_07_26-PM-06_42_38
Theory : minimal-first-order-logic
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