Nuprl Lemma : psub_transitivity
∀a,b,c:formula(). (a ⊆ b ⇒ b ⊆ c ⇒ a ⊆ c)
Proof
Definitions occuring in Statement :
psub: a ⊆ b,
formula: formula(),
all: ∀x:A. B[x],
implies: P ⇒ Q
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
so_lambda: λ2x.t[x],
member: t ∈ T,
implies: P ⇒ Q,
prop: ℙ,
so_apply: x[s],
psub: a ⊆ b,
pvar: pvar(name),
formula_ind: formula_ind,
all: ∀x:A. B[x],
subtype_rel: A ⊆r B,
pnot: pnot(sub),
or: P ∨ Q,
pand: pand(left;right),
por: por(left;right),
pimp: pimp(left;right),
guard: {T}
Lemmas referenced :
formula-induction,
all_wf,
formula_wf,
psub_wf,
equal-wf-T-base,
atom_subtype_base,
equal_wf,
pnot_wf,
or_wf,
pand_wf,
por_wf,
pimp_wf
Rules used in proof :
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isectElimination,
thin,
sqequalRule,
lambdaEquality,
hypothesis,
functionEquality,
hypothesisEquality,
independent_functionElimination,
lambdaFormation,
equalitySymmetry,
hyp_replacement,
Error :applyLambdaEquality,
baseApply,
closedConclusion,
baseClosed,
applyEquality,
atomEquality,
unionElimination,
dependent_functionElimination,
inrFormation,
inlFormation,
because_Cache
Latex:
\mforall{}a,b,c:formula(). (a \msubseteq{} b {}\mRightarrow{} b \msubseteq{} c {}\mRightarrow{} a \msubseteq{} c)
Date html generated:
2016_10_25-AM-11_21_27
Last ObjectModification:
2016_07_12-AM-07_27_52
Theory : general
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