Nuprl Lemma : dl-valid-trivial
∀phi:Prop. |= phi ⇒ phi
Proof
Definitions occuring in Statement :
dl-valid: |= phi,
dl-implies: x1 ⇒ x,
dl-prop: Prop,
all: ∀x:A. B[x]
Definitions unfolded in proof :
all: ∀x:A. B[x],
dl-valid: |= phi,
member: t ∈ T,
prop: ℙ,
uall: ∀[x:A]. B[x],
dl-prop-sem: [|phi|],
dl-sem: dl-sem(K;n.R[n];m.P[m]),
so_lambda: λ2x.t[x],
top: Top,
so_apply: x[s],
so_lambda: so_lambda(x,y,z,w.t[x; y; z; w]),
so_apply: x[s1;s2;s3;s4],
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
implies: P ⇒ Q,
subtype_rel: A ⊆r B
Lemmas referenced :
istype-nat,
istype-universe,
dl-prop_wf,
dl-ind-dl-implies,
istype-void,
dl-prop-sem_wf,
subtype_rel_self
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation_alt,
universeIsType,
hypothesisEquality,
functionIsType,
cut,
introduction,
extract_by_obid,
hypothesis,
universeEquality,
because_Cache,
thin,
instantiate,
sqequalHypSubstitution,
isectElimination,
sqequalRule,
isect_memberEquality_alt,
voidElimination,
applyEquality,
lambdaEquality_alt
Latex:
\mforall{}phi:Prop. |= phi {}\mRightarrow{} phi
Date html generated:
2019_10_15-AM-11_44_17
Last ObjectModification:
2019_03_26-AM-11_50_15
Theory : dynamic!logic
Home
Index